Average Error: 0.1 → 0.4
Time: 21.6s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\cos y}\right)\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\cos y}\right)\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r122935 = x;
        double r122936 = y;
        double r122937 = cos(r122936);
        double r122938 = r122935 * r122937;
        double r122939 = z;
        double r122940 = sin(r122936);
        double r122941 = r122939 * r122940;
        double r122942 = r122938 - r122941;
        return r122942;
}
↓
double f(double x, double y, double z) {
        double r122943 = x;
        double r122944 = y;
        double r122945 = cos(r122944);
        double r122946 = cbrt(r122945);
        double r122947 = r122946 * r122946;
        double r122948 = r122943 * r122947;
        double r122949 = expm1(r122946);
        double r122950 = log1p(r122949);
        double r122951 = r122948 * r122950;
        double r122952 = z;
        double r122953 = sin(r122944);
        double r122954 = r122952 * r122953;
        double r122955 = r122951 - r122954;
        return r122955;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \cos y - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

    \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} - z \cdot \sin y\]

  4. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} - z \cdot \sin y\]
  5. Using strategy rm

  6. Applied log1p-expm1-u0.4

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\cos y}\right)\right)} - z \cdot \sin y\]

  7. Final simplification0.4

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\cos y}\right)\right) - z \cdot \sin y\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))